Generalizations of mock theta functions

被引：0

作者：

Cui, Su-Ping ^{[1
]}

Gu, Nancy S. S. ^{[2
]}

Su, Chen-Yang ^{[3
]}

Xie, Matthew H. Y. ^{[4
]}

机构：

[1] Qufu Normal Univ, Sch Math Sci, Shandong 273100, Peoples R China

[2] Nankai Univ, LPMC, Ctr Combinator, Tianjin 300071, Peoples R China

[3] Tianjin Normal Univ, Coll Math Sci, Tianjin 300387, Peoples R China

[4] Tianjin Univ Technol, Coll Sci, Tianjin 300384, Peoples R China

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2024年 / 20卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Basic hypergeometric series; mock theta functions; universal mock theta functions; Appell-Lerch sums; RAMANUJAN LOST NOTEBOOK; APPELL-LERCH SUMS; IDENTITIES; FORMS;

D O I：

10.1142/S1793042124501161

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Mock theta functions were first introduced by Ramanujan in his last paper to Hardy. Moreover, some other mock theta functions were presented in his lost notebook. It is well known that all the classical mock theta functions can be expressed by the universal mock theta functions g(2)(x,q) and g(3)(x,q). In this paper, we establish some generalized mock theta functions and express them in terms of Appell-Lerch sums. Meanwhile, we show that some of Ramanujan's two-parameter mock theta functions are the special cases of these functions.

引用

页码：2395 / 2413

页数：19

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